Question

Robinson's preferences between apples (a) and bananas (b) are expressed by the following:

 

U = (a+2)^0.5(b+1)^0.5

 

(a) Show that Robinson's indifference curves are negatively sloped.

(b) Are they convex to the origin? Explain.

Answer 1

a)U = (a+2)^0.5(b+1)^0.5

Let (a+2) be x and (b+1) be y.

U becomes;

U=$x^{0.5}y^{0.5}$

$MU_{x}=0.5x^{-0.5}y^{0.5}$

$MU_{y}=0.5x^{0.5}y^{-0.5}$

$MRS=\frac{MU_{x}}{MU_{y}}$

MRS is the slope of the indifference curve at any single point along the curve.

$=$ $\frac{0.5x^{-0.5}y^{0.5}}{0.5x^{-0.5}y^{0.5}}=\frac{y}{x}$

b)The indifference curves will be convex to the origin because, as one consumes more of good y, they will consume less of good x.